Pochettino's side had won all four matches at their new £1 billion Tottenham Hotspur stadium.
But Antonio's clinical second half strike ended that run as the West Ham winger became the first visiting player to score in the plush arena.
Third placed Tottenham's second defeat in their last three Premier League games put a dent in their bid to finish in the top four.
They hold a three-point lead over fourth-placed Chelsea and are four points ahead of fifth placed Arsenal, with both teams in action on Sunday.
It was a frustrating warm-up for Tottenham's Champions League semi-final first leg against Ajax in north London on Tuesday.
Blaming Tottenham's hectic fixture list for their defeat, Pochettino said: "We cannot put away the circumstance. They arrived fresh and ready to compete, for us it is completely different.
"We were tired. We knew that it was going to be tough because it was a derby, but we have to move on.
"It was really tough today. We did not manage the ball properly. In the second half we conceded a lot of space for them to counter attack."
Conceding that Tottenham had hurt their hopes of qualifying for next season's Champions League, Pochettino added: "It is a fight, it is a race, with two games to play. We knew that before."
Third bottom Cardiff are three points from safety and would be effectively condemned to relegation if fourth bottom Brighton beat Newcastle later on Saturday.
A Brighton win would move them six points clear of Cardiff with a vastly superior goal difference and both teams having two games to play.
Cardiff had only themselves to blame for a lacklustre display against already relegated Fulham at Craven Cottage.
Former Liverpool forward Ryan Babel netted Fulham's winner when he took Cyrus Christie's pass and produced a superb finish from 25 yards in the 79th minute.
Neil Warnock's men almost snatched a draw in stoppage-time when Junior Hoilett side-footed against the bar.
Southampton sealed their survival in a dramatic 3-3 draw against south-coast rivals Bournemouth at St Mary's.
Shane Long scored the fastest goal in Premier League history after 7.69 seconds against Watford in midweek and the Irish forward struck again, this time after 12 minutes, to put Southampton ahead with a low shot.
Dan Gosling equalised for Bournemouth eight minutes later from Callum Wilson's pass and the visitors were in front in the 32nd minute.
David Brooks crossed for Wilson to fire home after Southampton goalkeeper Angus Gunn could only push it into his path.
James Ward-Prowse bagged Southampton's equaliser from 20 yards in the 55th minute and Matt Targett made it three in the 67th minute, his effort ranking as the 1000th scored in the Premier League this season.
Wilson salvaged a point for Bournemouth with his 86th minute equaliser, but Southampton, seven points above the bottom three, are assured of staying up.
Wolves gained a measure of revenge for their FA Cup semi-final defeat against Watford as they beat the Hornets 2-1 at Vicarage Road.
Mexico striker Raul Jimenez gave Wolves the lead in the 41st minute with a header from Diogo Jota's cross.
Andre Gray drew Watford level four minutes after half-time, but Jota won it for Wolves in the 77th minute as Nuno Espirito Santo's side consolidated seventh place.
Crystal Palace played out a dour goalless draw with Everton at Selhurst Park.